Surface Vibration of a Multilayered Elastic Medium due to Harmonic Concentrated Force

2011 ◽  
Author(s):  
Akindeji Ojetola ◽  
Hamid Hamidzadeh
Keyword(s):  
Fourier Transform ◽  
Elastic Medium ◽  
Three Dimensional ◽  
Concentrated Force ◽  
Double Complex ◽  
Concentrated Load ◽  
Propagator Matrix ◽  
Displacement Vectors ◽  
Bottom Interface ◽  
Similar Information

Dynamic response of a multi-layer elastic medium subjected to harmonic surface concentrated load is considered. In development of the analytical solution, the three-dimensional theory of elasto-dynamic is utilized for derivation of the governing partial differential equations for each layer. These equations are solved in the Fourier domain by employing the Double Complex Fourier Transform technique. In the analysis, each layer of the medium is assumed to be extended infinitely in the horizontal x and z directions and has uniform depth in the y direction and is considered to be linearly elastic, homogeneous, and isotropic. Utilizing the Integral Fourier Transform, displacements and stresses at any point in each layer can be determined in terms of boundary stresses for each layer. Also, the presented solution provides the relation between stress and displacement vectors for the top and bottom of each layer in matrix notation. By satisfying the compatibility of displacements and stresses for each interface, a propagator matrix relating displacements and stresses at the top of the medium to the bottom interface will be obtained. This relates the displacement and stress vector on the top surface to the bottom interface by eliminating similar information for the other interfaces. In this study, the displacements on the surface of the layered medium are computed for the two cases where the surface of the medium is subjected to a concentrated harmonic vertical or horizontal harmonic force.

The Elastic Sphere Under Concentrated Loads

1952 ◽  
Vol 19 (4) ◽  
pp. 413-421 ◽  
Author(s):  
E. Sternberg ◽  
F. Rosenthal
Keyword(s):  
Three Dimensional ◽  
Plane Boundary ◽  
Elastic Sphere ◽  
Concentrated Loads ◽  
Concentrated Force ◽  
Concentrated Load ◽  
Load Axis ◽  
Present Solution ◽  
Photoelastic Investigation ◽  
Axisymmetric Problems

Abstract This paper contains an exact solution for the stress distribution in an elastic sphere under two equal and opposite concentrated loads, applied at the end points of a diameter. The solution is based on the Boussinesq stress-function approach to axisymmetric problems and is represented as a sum of two solutions: A singular solution in closed form, and a series solution corresponding to surface tractions which are finite and continuous throughout the surface of the sphere. It is shown that the singularity at the points of application of the loads is not identical with that arising at a concentrated load acting normal to a plane boundary. The existence of pseudosolutions to the problem under consideration, as well as to concentrated-force problems in general, is illustrated, and the validity of the present solution is confirmed through a limit process applied to the case of tractions uniformly distributed over a portion of the boundary. The numerical results for the normal stress on the plane of symmetry perpendicular to the load axis, are compared with the corresponding stress values obtained in a recent three-dimensional photoelastic investigation of the same problem by Frocht and Guernsey (1).

scholarly journals Hyperspectral Three-Dimensional Fluorescence Imaging Using Snapshot Optical Tomography

Sensors ◽  
2021 ◽  
Vol 21 (11) ◽  
pp. 3652
Author(s):  
Cory Juntunen ◽  
Isabel M. Woller ◽  
Yongjin Sung
Keyword(s):  
Fourier Transform ◽  
3D Imaging ◽  
Optical Tomography ◽  
Three Dimensional ◽  
High Spectral Resolution ◽  
Functional Information ◽  
Fluorescent Beads ◽  
Different Depths ◽  
Projection Images ◽  
Imaging Performance

Hyperspectral three-dimensional (3D) imaging can provide both 3D structural and functional information of a specimen. The imaging throughput is typically very low due to the requirement of scanning mechanisms for different depths and wavelengths. Here we demonstrate hyperspectral 3D imaging using Snapshot projection optical tomography (SPOT) and Fourier-transform spectroscopy (FTS). SPOT allows us to instantaneously acquire the projection images corresponding to different viewing angles, while FTS allows us to perform hyperspectral imaging at high spectral resolution. Using fluorescent beads and sunflower pollens, we demonstrate the imaging performance of the developed system.

3D Profile Variety Measurement of Pectoral Fin in Fish Fast Start

2011 ◽  
Vol 83 ◽  
pp. 280-284
Author(s):  
Ming Jiang ◽  
Shu Zhang ◽  
Xiao Yuan He
Keyword(s):  
Fourier Transform ◽  
High Speed ◽  
Kinetic Characteristic ◽  
Three Dimensional ◽  
Pectoral Fin ◽  
Fourier Transform Profilometry ◽  
Fast Start ◽  
Fringe Patterns ◽  
3D Information ◽  
3D Profile

Fast-starts are brief, sudden accelerations used by fish during predator-prey encounters. In this paper, a three-dimensional (3D) test and analysis method is critical to understand the function of the pectoral fin during maneuvers. An experiment method based on Fourier Transform Profilometry for 3D pectoral fin profile variety during fish maneuvers is proposed. This method was used in a carp fast-start during prey. Projecting the moiré fringes onto a carp pectoral fin it will produce the deformed fringe patterns contain 3D information. A high speed camera captures these time-sequence images. By Fourier transform, filter, inverse Fourier transform and unwrap these phase maps in 3D phase space, the complex pectoral fin profile variety were really reconstructed. The present study provides a new method to quantify the analysis of kinetic characteristic of the pectoral fin during maneuvers.

Bending of an Infinite Beam on an Elastic Foundation

1937 ◽  
Vol 4 (1) ◽  
pp. A1-A7 ◽  
Author(s):  
M. A. Biot
Keyword(s):  
Elastic Foundation ◽  
Poisson Ratio ◽  
Elementary Theory ◽  
Three Dimensional ◽  
Bending Moment ◽  
Two Dimensional ◽  
Concentrated Load ◽  
Elastic Continuum ◽  
Infinite Beam ◽  
A Value

Abstract The elementary theory of the bending of a beam on an elastic foundation is based on the assumption that the beam is resting on a continuously distributed set of springs the stiffness of which is defined by a “modulus of the foundation” k. Very seldom, however, does it happen that the foundation is actually constituted this way. Generally, the foundation is an elastic continuum characterized by two elastic constants, a modulus of elasticity E, and a Poisson ratio ν. The problem of the bending of a beam resting on such a foundation has been approached already by various authors. The author attempts to give in this paper a more exact solution of one aspect of this problem, i.e., the case of an infinite beam under a concentrated load. A notable difference exists between the results obtained from the assumptions of a two-dimensional foundation and of a three-dimensional foundation. Bending-moment and deflection curves for the two-dimensional case are shown in Figs. 4 and 5. A value of the modulus k is given for both cases by which the elementary theory can be used and leads to results which are fairly acceptable. These values depend on the stiffness of the beam and on the elasticity of the foundation.

A Fast Method for Solving Contact Plasticity in a Half Space

2011 ◽  
Author(s):  
Zhanjiang Wang ◽  
Xiaoqing Jin ◽  
Shuangbiao Liu ◽  
Leon M. Keer ◽  
Jian Cao ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Residual Stresses ◽  
Fast Fourier Transform ◽  
Half Space ◽  
Three Dimensional ◽  
New Method ◽  
Fast Method ◽  
Discrete Convolution ◽  
Influence Coefficients ◽  
The One

This paper presents a new method of contact plasticity analysis based on Galerkin vectors to solve the eigenstresses due to eigenstrain. The influence coefficients relating eigenstrains to eigenstresses thus can be divided into four terms the one due to the eigenstrains in the full space, others due to the mirrored eigenstrains in the mirror half space. Each term can be solved fast and efficient by using the three-dimensional discrete convolution and fast Fourier transform (DC-FFT) or the three-dimensional discrete correlation and fast Fourier transform (DCR-FFT). The new method is used to analyze the contact plastic residual stresses in half space.

scholarly journals PENGARUH WAKTU CURING TERHADAP KUAT TEKAN GEOPOLIMER BERBASIS FLY ASH

2019 ◽  
Vol 2 (1) ◽  
pp. 50
Author(s):  
Andrie Harmaji ◽  
Claudia Claudia ◽  
Lia Asri ◽  
Bambang Sunendar ◽  
Ahmad Nuruddin
Keyword(s):  
Compressive Strength ◽  
Fourier Transform ◽  
Fly Ash ◽  
Power Plant ◽  
Functional Groups ◽  
Room Temperature ◽  
Three Dimensional ◽  
Fine Aggregate ◽  
Alkali Activator ◽  
Infra Red

Abstract:. Suralaya power plant produces fly ash about 219.000 ton per year. Fly ash contents of silica and alumina as major components that can be used as precursors for geopolymer, a three dimensional networks aluminosilicate polymers. This research aim is to utilize fly ash for geopolymer made by mixing fly ash, fine aggregate, and alkali activator in a cubic mould and curing was carried out at room temperature for 7 and 28 days. After 28 days of curing the compressive strength of geopolymer reached 41.70 MPa. XRD characterization shows Albite (NaAlSi3O8) formation which has similarity to geopolymer compound. Fourier Transform Infra Red spectra show siloxo and sialate bond. These are typical functional groups that are found in geopolymer materials.Keyword: geopolymer, fly ash, aluminosilicate, alkali activator, albite, siloxo, sialateAbstrak: Pembangkit Listrik Tenaga Uap (PLTU) Suralaya menghasilkan fly ash (abu terbang) sekitar 219.000 ton per tahun. Fly ash memiliki silika dan alumina sebagai komponen utama yang dapat digunakan sebagai prekursor untuk geopolimer, suatu material polimer aluminosilikat tiga dimensi. Penelitian ini bertujuan untuk memanfaatkan fly ash untuk geopolimer yang dibuat dengan mencampur fly ash, agregat halus, dan aktivator alkali dalam cetakan kubik dan pengawetan dilakukan pada suhu kamar selama 7 dan 28 hari. Setelah 28 hari curing kekuatan tekan geopolimer mencapai 41,70 MPa. Karakterisasi XRD menunjukkan pembentukan Albite (NaAlSi3O8) yang memiliki kemiripan dengan senyawa geopolimer. Hasil spektroskopi Fourier Transform Infra Red (FTIR) menunjukkan ikatan siloxo dan sialate yang merupakan gugus fungsional khas yang ditemukan dalam geopolimer.Kata Kunci: geopolimer, abu terbang, aluminosilikat, alkali aktivator, albite, siloxo, sialate

scholarly journals ANALISIS PENGARUH BENTUK DAN LOKASI BUKAAN PADA BALOK TINGGI MENGGUNAKAN METODE ELEMEN HINGGA

2020 ◽  
Vol 3 (4) ◽  
pp. 1209
Author(s):  
Anthony Fariman ◽  
Leo S. Tedianto
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Wall Structure ◽  
Deep Beam ◽  
Stress Distributions ◽  
Stress Concentrations ◽  
Offshore Structure ◽  
Deep Beams ◽  
Concentrated Load ◽  
Cable Networks

ABSTRAKBalok tinggi beton bertulang merupakan salah satu struktur khusus yang dapat memikul beban cukup besar dan umumnya digunakan sebagai transfer girder, struktur lepas pantai, struktur dinding, dan pondasi. Kehadiran bukaan pada balok tinggi dapat memfasilitasi jalur saluran AC, saluran pipa, jaringan kabel dan lain-lain. Dengan adanya bukaan pada balok tinggi dapat memberikan beberapa efek samping yaitu terjadinya diskontinuitas geometri, tegangan terdistribusi non-linier pada balok tinggi, berkurangnya kekuatan dari balok, dan timbulnya konsentrasi tegangan di sekitar bukaan. Penelitian ini bertujuan untuk menganalisis efek dari kehadiran bukaan pada balok tinggi di atas dua perletakan (sendi-rol) dan dibebani beban terpusat di tengah bentang balok lalu memvariasikan bentuk bukaan (persegi, persegi panjang, dan lingkaran) dan lokasi bukaan. Tegangan lentur pada balok tinggi dan konsentrasi tegangan yang terjadi di sekitar bukaan merupakan hal yang akan dibahas dalam penelitian. Analisis akan dibantu dengan Midas FEA yang merupakan program berbasis elemen hingga dan  pemodelan dilakukan dengan elemen solid tiga dimensi. Hasil dari analisis ini menunjukkan bahwa kehadiran bukaan pada balok tinggi menyebabkan kenaikan tegangan secara signifikan. Lokasi dari bukaan yang mendekati daerah tengah bentang balok juga sangat mempengaruhi besarnya tegangan yang terjadi.ABSTRACTReinforced concrete deep beam is one of the special structures that can carry quite a big load and generally used as a transfer girder, offshore structure, wall structure, and foundation. The appearance of openings in deep beams can facilitate AC pipelines, plumbing pipes, cable networks, etc. The existence of openings in deep beams can provide a few side effects such as geometric discontinuity, non-linear stress distributions over the deep beams, reduced strength of the deep beams, and stresses concentration will emerged around the openings. The purpose of this research is to analyze the effects from the existence of openings in deep beams on two supports (hinge and roller) and loaded by concentrated load in mid-span then variate the shape of openings (square, rectangle, and circle) and location of the openings. Flexural stresses in deep beams and the stress concentrations that occur around the openings are discussed in this research. The analysis will be assisted by Midas FEA which is a finite element based program and modelling will be executed in three dimensional solid elements. The result of this analysis showed that the existence of the openings in deep beams can cause stresses to increase significantly high. The location of the openings close to the mid-span of the deep beams also affect the amount of the stresses that occurs.

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